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Fifth International Conference on Dynamic Systems and Applications
May 30 - June 2, 2007
Morehouse College
Atlanta, Georgia, USA

Organizers
M. Sambandham, Morehouse College, IFNA

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Differential equations for solving an inverse optimization problems
by
Anatoly Antipin
Computing Center of Russian Academy of Sciences

Abstract

We represent recent results connected with development of dynamics for solving of inverse optimization problems. These problems can be formulated as a systems composed by means of parametric convex programming problems and identical mappings. More precisely we consider parametric convex problem, where a vector of the right-hand part of functional constraints is a parameter such that the area of its values is positive orthant from finite dimensional Euclidean space. Movement of parameter generates a sensitivity function or a optimal value function. This function is convex and subdifferentiated, its subdifferential is a monotone and multiple-valued mapping. It is possible to consider the graph of this mapping and the identical one. A point of crossing of two graphs for their mappings is a solution of a inverse optimization problem. This point is also a fixed one of a vector field which is generated by difference of both above-mentioned mappings. In talk it is offered to construct dynamics (system of the differential equations) such that the trajectory of it will be converged to fixed point of the vector field or to a solution of a inverse optimization problem. Convergence of this trajectory is proved. Economic interpretation of this inverse problem as model of deficiency of resources is given.

Date received: February 11, 2007

Copyright © 2007 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # catb-88.